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BINARY DIVISION
Binary division is similar to decimal division. It starts on the left side of the numbers.
Example 1 Example 2 Example 3
Compute (101) ÷ (10) 2 Compute (1111) ÷ (11) 2 Compute (101101) ÷ (101) 2
2
2
2
1 0 quotient 1 0 1 quotient 1 0 0 1 quotient
1 0 1 0 1 dividend 1 1 1 1 1 1 dividend 1 0 1 1 0 1 1 0 1 dividend
– 1 0 – 1 1 – 1 0 1
1 0 0 1 0 1
– 0 0 – 0 0 – 0 0
1 remainder 1 1 1 0
– 1 1 – 0 0
0 remainder 1 0 1
– 1 0 1
0 remainder
Try This
Computational Skills
Compute the following as directed:
(a) (1011) + (1001) _______________
2 2
(b) (11011) – (10101) _______________
2 2
(c) (1101) × (110) _______________
2 2
(d) (11001) ÷ (101) _______________
2 2

Knowledge Discovery Subject Enrichment
Apart from Decimal and Binary number systems, two more number systems are used in computer
systems. The Octal number system, with base 8, uses digits 0 – 7. Octal numbers are used to represent file
permissions in the UNIX operating system. The Hexadecimal number system, with base 16, uses digits
0 – 9 and letters A – F. Hexadecimal numbers are used to represent memory locations, colours on web
pages, error messages, and Media Access Control (MAC) addresses.

Database Subject Enrichment

Numbers are of different types and often have interesting properties. Some special numbers are described
below:
• An Armstrong number of three digits is an integer such that the sum of the cubes of its digits is equal
to the number itself. The smallest Armstrong number is 153.
153 = 1 + 5 + 3 = 1 + 125 + 27
3
3
3
• A Perfect number is a positive integer that is equal to the sum of its positive proper factors less than
itself. The smallest perfect number is 6. The positive proper factors of 6 are 1, 2, and 3.
1 + 2 + 3 = 6
• A Harshad/Niven number is a positive integer that is divisible by the sum of its own digits. All
one-digit numbers are Harshad/Niven numbers. The smallest two-digit Harshad/Niven number is 10.
1 + 0 = 1 and 10 ÷ 1 = 10

10